- #1

#### JaysFan31

## Homework Statement

Let V=Mn(F) be the space of all nxn matrices over F; define TA=(1/2)(A+transpose(A)) for A in V.

Verify that T is not only a linear operator on V, but is also a projection.

## Homework Equations

A is a projection when A squared=A.

## The Attempt at a Solution

I don't see how this works since clearly (1/2)(A+transpose(A)) squared does not equal (1/2)(A+transpose(A)) for all matrices.

What am I doing wrong?